| http://dbpedia.org/ontology/abstract
|
In mathematics, logarithmic Sobolev inequa … In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient . These inequalities were discovered and named by Leonard Gross, who established them in dimension-independent form, in the context of constructive quantum field theory. Similar results were discovered by other mathematicians before and many variations on such inequalities are known. Gross proved the inequality: where is the -norm of , with being standard Gaussian measure on Unlike classical Sobolev inequalities, Gross's log-Sobolev inequality does not have any dimension-dependent constant, which makes it applicable in the infinite-dimensional limit. In particular, a probability measure on is said to satisfy the log-Sobolev inequality with constant if for any smooth function f where is the entropy functional.unction f where is the entropy functional.
|
| http://dbpedia.org/ontology/wikiPageExternalLink
|
https://projecteuclid.org/euclid.dmj/1077311187 +
|
| http://dbpedia.org/ontology/wikiPageID
|
64602455
|
| http://dbpedia.org/ontology/wikiPageLength
|
2313
|
| http://dbpedia.org/ontology/wikiPageRevisionID
|
1117757675
|
| http://dbpedia.org/ontology/wikiPageWikiLink
|
http://dbpedia.org/resource/Category:Axiomatic_quantum_field_theory +
, http://dbpedia.org/resource/Gaussian_measure +
, http://dbpedia.org/resource/Mathematics +
, http://dbpedia.org/resource/Category:Sobolev_spaces +
, http://dbpedia.org/resource/Constructive_quantum_field_theory +
, http://dbpedia.org/resource/Leonard_Gross +
, http://dbpedia.org/resource/Sobolev_inequalities +
, http://dbpedia.org/resource/Category:Logarithms +
|
| http://dbpedia.org/property/wikiPageUsesTemplate
|
http://dbpedia.org/resource/Template:Citation +
, http://dbpedia.org/resource/Template:Short_description +
, http://dbpedia.org/resource/Template:Reflist +
|
| http://purl.org/dc/terms/subject
|
http://dbpedia.org/resource/Category:Logarithms +
, http://dbpedia.org/resource/Category:Axiomatic_quantum_field_theory +
, http://dbpedia.org/resource/Category:Sobolev_spaces +
|
| http://www.w3.org/ns/prov#wasDerivedFrom
|
http://en.wikipedia.org/wiki/Logarithmic_Sobolev_inequalities?oldid=1117757675&ns=0 +
|
| http://xmlns.com/foaf/0.1/isPrimaryTopicOf
|
http://en.wikipedia.org/wiki/Logarithmic_Sobolev_inequalities +
|
| owl:sameAs |
https://global.dbpedia.org/id/DF8N4 +
, http://dbpedia.org/resource/Logarithmic_Sobolev_inequalities +
, http://www.wikidata.org/entity/Q97610260 +
|
| rdfs:comment |
In mathematics, logarithmic Sobolev inequa … In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient . These inequalities were discovered and named by Leonard Gross, who established them in dimension-independent form, in the context of constructive quantum field theory. Similar results were discovered by other mathematicians before and many variations on such inequalities are known. Gross proved the inequality: In particular, a probability measure on is said to satisfy the log-Sobolev inequality with constant if for any smooth function fwith constant if for any smooth function f
|
| rdfs:label |
Logarithmic Sobolev inequalities
|
